Photo-Ionization in the Soft x-Ray Range: 1ZDependence in a Central-Potential Model

Using a one-electron model with a Herman-Skillman central potential, photo-ionization calculations have been performed which emphasize the soft x-ray spectral range (∼100 eV to ∼2 keV). The $M_{\mathrm{II},\mathrm{III}}\mathrm{}\left(3p\right)\mathrm{}$ subshell was studied in Ar, Cu, and Ge, as well as the $M_{\mathrm{IV},\mathrm{V}}\mathrm{}\left(3d\right)\mathrm{}$ and $M_{\mathrm{II},\mathrm{III}}$ in Kr, Rh, Xe, Eu, Au, and Fm in an effort to explain the combined $Z$ and energy dependence of the photo-ionization cross sections for these subshells. In addition, calculations have been performed for $3s$, $4s$, $5s$, $4p$, $5p$, $4d$, $5d$, and $4f$ subshells in certain elements. The results, which are considerably different from the predictions of the hydrogenlike model, show certain regularities which are explained in terms of the potentials. Comparisons with experiment show that the model correctly predicts the gross spectral shape of photo-ionization cross sections, but the results are somewhat inaccurate in the vicinity of large absorption peaks. This calculation is considered to be a first approximation which can be improved by taking exchange into account more exactly and by including electron-electron correlation.